The most common and most likely answer to this crossword clue is the 4 plus 3 plus 4 letter word OVER THE HUMP
I've seen this crossword clue in The Daily Telegraph
O
V
E
R
T
H
E
H
U
M
P
Buddy explains!
The straight part
We know that "Past the difficulty" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case past the difficulty = over the hump.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.